Problem
Now that I have seen that the percentage of drivers involved in a
collision
decreases as age increases, tests should be done to see if there is
a linear
relationship. That is, what is the equation of the line of best fit?
Then a
correlation coefficient needs to be determined to see how well the
line fits.
Plan
To determine the line of best fit, y= a + bx, x and y must first be
defined. Then
numerous calculations need to be done concerning the sum of squares.
Using
the values calculated to determine the equation of the line of best
fit, a
correlation coefficient will be determined.
Data
Let x be the midpoint for each of the age groups. Let y be the percentage
of
drivers involved in a collision.
Analysis
The following calculations were made with Fathom:
Therefore the equation of the line of best fit is:
% of drivers involved in collisions = 8.628 - 0.0826
x.
To see how well the line fits, a correlation
coefficient, r, needs to be calculated. The correlation coefficient
was calculated with Fathom.
The closer |r| is to 1, the stronger the correlation
and since -1<r<1 and the correlation coefficient for the line
of best fit is -0.984 there exists a strong negative correlation.
Therefore, y = 8.628 - 0.0826 x fits the data very well. The following
is a graph showing the original scatter plot including the Line of
Best Fit.
Conclusion
There exists a linear relationship between the percentage of drivers
involved in an accident and age. The equation of the line of best
fit is percentage = 8.628 - 0.0826 age. The correlation coefficient
is -0.984.
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